In a commercial nuclear power plant, for example, in a pressurized water reactor (hereinafter referred to as “PWR” in principle), in order to ensure safe and cost-efficient operation, reactor core design is carried out before each cycle of operation to consider various matters such as how to arrange fuel assemblies each having different burn-up and hence different reactivity in the reactor core and whether or not self-regulating characteristics of the reactor core are sufficient.
During periodic inspections between each cycle, nuclear reactor physics tests (start-up reactor physics tests) are performed to measure and evaluate reactor physics characteristics of the reactor core for the current cycle operation. For example, during the tests, whether or not the designed reactor core achieves critical through prescribed operations is determined, and reactivity variation when control rods are moved with respect to the reactor core and reactivity variation when moderator temperature is changed are measured, to confirm the validity of the reactor core design.
Here, the self-regulating characteristics refer to characteristics that when reactivity of the reactor core varies by some cause or other and s as a result, a phenomenon acting in the reverse direction naturally occurs in the reactor, that is, so-called negative reactivity feedback, which is a very important factor ensuring safe operation of a nuclear reactor. In a PWR, fuel temperature reactivity coefficient, that is, reactivity variation of the nuclear reactor caused by fuel temperature variation, and moderator temperature reactivity coefficient, that is, reactivity variation of the nuclear reactor derived from moderator temperature variation, are both negative (if the temperature rises, negative reactivity is added), and thus the PWR exhibits the self-regulating characteristics. In a boiling water reactor (hereinafter referred to as “BWR” in principle), the self-regulating characteristics are exhibited additionally by the phenomenon (effect) that the number of neutrons slowed down by cooling water decreases, as the bubbles in the cooling water increases when temperature rises.
The fuel temperature reactivity coefficient mentioned above is governed by a phenomenon called Doppler effect. Doppler effect refers to a phenomenon that if temperature rises, nuclide existing in the fuel increases resonance absorption of neutrons, so that the number of neutrons contributing to nuclear fission decreases and, as a result, core reactivity lowers. The ratio of the reactivity variation to unit temperature change is referred to as Doppler reactivity coefficient. In U238 that occupies a great part of uranium fuel used in existing light water reactors, the effect is significant since U238 exhibits strong resonance absorption of neutrons. This effect realizes the function of decreasing reactor power if the temperature of nuclear fuel increases. In addition, this effect realizes rapid time response, since it reflects temperature variation of fuel more directly in a short period after reactor power variation rather than that of the moderator. Hence, in a PWR, this effect is believed to play a key role in realizing safe operation, since PWR lacks the effect attained by the increase of bubbles in cooling water, which is attained in a BWR
The relation between the fuel temperature variation and the reactivity in a commercial nuclear power plant is evaluated by using, temperature dependent nuclear reactor cross section data obtained by measurements of relation between the nuclear fuel temperature variation and nuclear reaction such as neutron absorption. It is noted, however, that in the nuclear reactor physics tests, the fuel temperature reactivity coefficient is not directly measured, since it is difficult to directly measure the fuel temperature and if fuel temperature is changed, other parameters including the moderator temperature would also be changed. Conventionally Doppler reactivity coefficient is evaluated by neutronics characteristics analysis at the time of nuclear core design.
As long as the conventional fuel are used, Doppler reactivity coefficient can be evaluated with high accuracy based on knowledge and experiences accumulated for a long history (paragraphs 0003 and 0004 of Patent Document 1).
In order to realize safe operation of nuclear reactor with higher reliability, it is preferred to directly measure Doppler reactivity coefficient, as part of the verification of core design. It is more important particularly for PWRs, in which full-scale utilization of MOX fuel and high burn-up fuel within a few years is planned.
In countries outside Japan, direct measurements of the relation between fuel temperature variation and reactivity variation, that is, fuel temperature reactivity coefficient, were made several times in 1950s in research reactors. In such measurements, temperature of small spheres made of metal uranium or uranium oxide was increased under soft neutron spectrum conditions with few fast neutrons, and reactivity variation was measured (Non-Patent Documents 1 and 2).
In Japan, using FCA (Fast Critical Assembly: very small nuclear reactor) of Japan Atomic Energy Agency, in 2005, only the uranium oxide fuel or MOX fuel was loaded in soft neutron spectrum field, temperature was increased and reactivity variation was measured (Non-Patent Document 3).
The data obtained by the above-described measurements using actual reactors and the like are important for expanding database and for verifying general-purpose nuclear design codes. However, the nuclear reactors used for the actual measurements are very small and much different in shape and structure from commercial nuclear power plants. Therefore, the validity of core design and the verification of code design codes directed to large scale commercial nuclear power plants that require higher accuracy are attained not directly but indirectly.
For this reason, technology that enables direct measurement of Doppler reactivity coefficient particularly of a PWR has been long desired. Tsuji, one of the inventors of the present invention, at last developed the method recently (Patent Document 1).
According to this method, basically, isothermal temperature reactivity coefficient measurement method and dynamic identification are combined for measuring fuel temperature reactivity coefficient. Generally, the method includes the steps (process steps) described below.
Here, “isothermal temperature reactivity coefficient” refers to the sum of reactivity coefficient related to fuel temperature only (obtained by partial differentiation by fuel temperature) and reactivity coefficient related to moderator temperature only (obtained by partial differentiation by moderator temperature).
In the isothermal temperature reactivity coefficient measurement, moderator temperature is slowly increased or decreased without fission energy while the nuclear reactor is in critical but substantially zero power state. In this experiment, fuel temperature follows quasi-statically or isothermally moderator temperature (this means that fuel temperature is nearly equal to moderator temperature), because the fission energy is negligible and the changing rate of moderator temperature is very slow. As the temperatures change, the reactivity also changes.
First, form the measurement mentioned above, the isothermal temperature reactivity coefficient is obtained as the ratio of reactivity variation to moderator temperature variation.
Next, control rods are withdrawn to add external reactivity, whereby reactor power is increased, for example, by about 1% of the rated power.
At this time, time changes of added external reactivity, ex-core neutron detector response, inlet coolant (moderator) temperature and average coolant (moderator) temperature are measured and time-series data of them are collected.
Further the ex-core neutron detector response is input to a digital reactivity meter, to obtain transient of nuclear reactor reactivity.
From the resulting time-series data, fuel temperature reactivity coefficient is calculated using dynamic identification.
Specifically, the measured time series data are converted into frequency response expressions by numerical Fourier Transform to apply a dynamic identification method in a frequency domain. Doppler reactivity coefficient is determined so as to reproduce the frequency responses of measured data in the frequency transfer response of the reactor kinetics model through the least square fitting (basically, by the least square method).
It is note that moderator temperature reactivity coefficient can be calculated by subtracting Doppler reactivity coefficient from isothermal temperature reactivity coefficient.
Dynamics Identification in a frequency domain refers to a method of estimating a frequency transfer function G(ω) that establishes a frequency response relation between the input and output frequency responses, u(ω) and x(ω) at the frequency ω that are converted from time series data u(t) and x(t) by numerical Fourier Transform, and thereby finding g(t) (solving the function equation), when a known function u(t) is input to a fully or partially unknown function g(t) and an output function x(t) is known,    Patent Document 1: JP2006-84181A    Non-Patent Document 1: E. Creutz, et al., “Effect of Temperature on Total Resonance Absorption of Neutrons by Spheres of Uranium Oxide,” J. Apple. Phys. 26, 276 (1955)    Non-Patent Document 2: R. M. Pearce et al., “A Direct Measurement Uranium Metal Temperature Coefficient of Reactivity,” Nucl. Sci. Eng., 2, 24 (1957)    Non-Patent Document 3: JAERI-Research, 2005-026 issued by Japan Atomic Energy Agency